Equitable colorings of -corona products of cubic graphs

A graph G is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest integer k for which such a coloring exists is known as the equitable chromatic number of G and it is denoted by...

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Vydáno v:Archives of control sciences Ročník 34; číslo No 1; s. 211 - 223
Hlavní autoři: Furmańczyk, Hanna, Kubale, Marek
Médium: Journal Article
Jazyk:angličtina
polština
Vydáno: Polish Academy of Sciences 29.03.2024
Témata:
1-absolute approximation algorithm
corona graph
corona products
cubic graph
equitable chromatic number
polynomial algorithm
ISSN:1230-2384
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Shrnutí:A graph G is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest integer k for which such a coloring exists is known as the equitable chromatic number of G and it is denoted by x=( G). In this paper the problem of determining the value of equitable chromatic number for multicoronas of cubic graphs G◦ lH is studied. The problem of ordinary coloring of multicoronas of cubic graphs is solvable in polynomial time. The complexity of equitable coloring problem is an open question for these graphs. We provide some polynomially solvable cases of cubical multicoronas and give simple linear time algorithms for equitable coloring of such graphs which use at most x=( G◦ lH) + 1 colors in the remaining cases.
ISSN:1230-2384
DOI:10.24425/acs.2024.149658